Method and apparatus to detect faults in rotary machines

ABSTRACT

A method and an apparatus are disclosed to detect faults in a rotary machine having a rotor and at least two stator windings. The method comprises generating an input signal and applying the input signal to stator windings while the rotor is locked at a rotor position, measuring output signals from the stator windings and processing all the output signals by Fourier transform to obtain frequency responses of the stator windings, forming derived quantities from all the frequency responses so that the derived quantities are independent of the rotor position, comparing the derived quantities with corresponding reference quantities, determining that there is a fault in the rotary machine if a magnitude or phase difference between the derived quantities and the corresponding reference quantities exceeds a threshold number. The apparatus is designed to test a rotary machine using the inventive method.

FIELD OF THE INVENTION

The present invention relates to a method and apparatus to detect faultsin a rotary machine, specifically an electric rotary machine with arotor and at least two stators.

BACKGROUND ART

An electric rotary machine can be an electric motor or a generator.

Electric motor is widely used in both industrial and consumer productssuch as pumps, compressors and fans. It is important to identify anypotential faults in an electric motor and maintain it in good health.The failure modes of an electric motor include stator turn-turn short,broken stator windings, stator-frame insulation breakdown, deterioratedrotor eccentricity, broken rotor bars, rotor bar-bar short, shiftedshaft, and bearing defects.

Fault detection techniques of a rotary machine mainly fall into twocategories, online test and offline test. Online test is to measuredynamics of a rotary machine while the rotary machine is in operation.Online test typically requires various types of sensors and the outputis also vulnerable to noise. Offline test is to measure statics of arotary machine and it is more immune to noise. Offline tests can be lowvoltage, medium voltage and high voltage.

Frequency response is a digital signal processing (DSP) technique touniquely identify a system. It is like a system's fingerprint and is apowerful tool to identify abnormality in a system. IEC 60076-18standardizes the Sweep Frequency Response Analysis (SFRA) technique tomeasure frequency response of power transformers to detect faults. Whilethere are similarities between power transformers and rotary machines,there is no standard for rotary machine testing based on frequencyresponse. Additionally, IEC 60076-18 does not describe how to properlyinterpret the test data from SFRA.

The difficulty of applying frequency response method in rotary machinefault detection lies in the fact that the frequency response isdependent on the rotor position. There have been attempts to apply theSFRA technique on rotary machines: L. Lamarre and P. Picher: “Impedancecharacterization of hydro generator stator windings and preliminaryresults of FRA analysis”, Proc. Conf. Record 2008, IEEE Int. Symp.Electr. Insul., pp. 227-230 (publication [1]); Martin Brandt, SlavomírKascak: “Failure Identification of Induction Motor using SFRA Method”,ELEKTRO 2016, pp 269-272 (publication [2]). However, either the rotorhas to be removed or the rotor has to be set at a known position.Further, bulky and expensive equipment has to be used. This hascomplicated the test and analysis, and made it difficult to implement.

Thus, there remains a considerable need for methods and apparatus thatcan reliably and conveniently test rotary machines.

SUMMARY OF THE INVENTION

A primary object of the present invention is to provide a reliable andpractical method to detect faults in electric rotary machines,eliminating the requirement that rotor has to be tested at a knownposition.

Another object of the present invention is to provide a reliable andsystematic method to interpret the test data and eliminate thesubjective judgment and errors in evaluating rotary machine state.

An additional object of the present invention is to provide a convenientapparatus to implement the inventive method.

In a first aspect of the invention, a method to detect faults in arotary machine having a rotor and at least two stator windings isprovided. The method comprises the following steps:

generating an input signal and applying the input signal to statorwindings while the rotor is stationary at a position,

measuring an output signal from the stator windings at the sameposition, processing all the output signals to obtain a frequencyresponse of the rotary machine at the same position,

calculating a derived quantity from all the frequency responses so thatthe derived quantity is independent of rotor position,

comparing the derived quantity with a corresponding reference quantityusing a statistical method,

determining that there is a fault in the rotary machine if there is adifference between the derived quantity and the corresponding referencequantity.

The input signal comprises an arbitrary waveform including a sweepingfrequency waveform, an impulse waveform, a maximum length binarysequence (MLBS) waveform and other wideband waveforms.

The output signal comprises at least a current or a voltage of thestator windings.

The frequency response can be calculated by relating the output signalto the input signal using Kirchhoff equations.

The number of derived quantity can be one to N−1, where N is the numberof the stator windings.

An advantage of the inventive method is that the rotary machine can betested at any rotor position, which significantly simplifies the test.Furthermore, the derived quantity is independent of rotor position,which removes the ambiguity in interpreting the data.

The reference quantity can be derived while the rotor is stationary atanother position.

The reference quantity can also be derived in a different time period.

The reference quantity can be derived on a reference rotary machine aswell.

Advantageously, there are multiple ways to compare a derived quantitywith the corresponding reference quantity. Furthermore, there is one ormore than one derived quantity to be compared, for example, there aretwo derived quantities for a three-phase rotary machine, which makes itmore robust in deciding if there is a fault in the rotary machine.Additionally, the comparison covers a wide range of frequencies for eachderived quantity. Depending on the failure mode, the derived quantitycan be more sensitive at a certain frequency, which increases thesensitivity of the detection.

The statistical method comprises statistical hypothesis tests, meancomparison, standard deviation comparison, and other statisticalcomparison methods. The statistical hypothesis tests include Student'st-test, F-test, and analysis of variance (ANOVA).

The statistical hypothesis test is a well-established method to comparetwo populations. With statistical hypothesis test applied herein, thesubjective judgment and errors are eliminated in evaluating the state ofa rotor machine. Moreover, a confidence level is provided if statisticalhypothesis test shows significant difference between a derived quantityand the corresponding reference quantity. Therefore, the user has moreconfidence in evaluating the rotary machine state.

In a second aspect of the invention, an apparatus to detect faults in arotary machine having a rotor and at least two stator windings isprovided. The apparatus comprises the following functions:

generating an input signal and applying the input signal to statorwindings while the rotor is stationary at a position,

measuring an output signal from the stator windings at the sameposition, processing all the output signals to obtain a frequencyresponse of the rotary machine at the same position,

calculating a derived quantity from all the frequency responses so thatthe derived quantity is independent of rotor position,

comparing the derived quantity with a corresponding reference quantityusing a statistical method,

determining that there is a fault in the rotary machine if there is adifference between the derived quantity and the corresponding referencequantity.

The input signal comprises an arbitrary waveform including a sweepingfrequency waveform, an impulse waveform, a maximum length binarysequence (MLBS) waveform and other wideband waveforms.

The output signal comprises at least a current or a voltage of thestator windings.

The frequency response can be calculated by relating the output signalto the input signal using Kirchhoff equations.

The number of derived quantity can be one to N−1, where N is the numberof the stator windings.

An advantage of the inventive apparatus is that the rotary machine canbe tested at any rotor position, which significantly simplifies the testand apparatus design. Furthermore, the derived quantity is independentof rotor position, which removes the ambiguity in interpreting the data.

The reference quantity can be derived while the rotor is stationary atanother position.

The reference quantity can also be derived in a different time period.

The reference quantity can be derived on a reference rotary machine aswell.

Advantageously, there are multiple ways to compare a derived quantitywith the corresponding reference quantity. Furthermore, there is one ormore than one derived quantity to be compared, for example, there aretwo derived quantities for a three-phase rotary machine, which makes itmore robust in deciding if there is a fault in the rotary machine.Additionally, the comparison covers a wide range of frequencies for eachderived quantity. Depending on the failure mode, the derived quantitycan be more sensitive at a certain frequency, which increases thesensitivity of the detection.

The statistical method comprises statistical hypothesis tests, meancomparison, standard deviation comparison, and other statisticalcomparison methods. The statistical hypothesis tests include Student'st-test, F-test, and analysis of variance (ANOVA).

The statistical hypothesis test is a well-established method to comparetwo populations. With statistical hypothesis test applied herein, thesubjective judgment and errors are eliminated in evaluating rotarymachine state. Moreover, a confidence level is provided if statisticalhypothesis test shows significant difference between a derived quantityand the corresponding reference quantity. Therefore, the user has moreconfidence in evaluating the rotary machine state.

Numerous features, aspects, and advantages of the present invention willbecome more apparent from the following detailed description of apreferred embodiment of the invention, along with the accompanyingdrawing.

BRIEF DESCRIPTION OF THE DRAWING

To facilitate understanding embodiments of the present invention,reference is now made to the following exemplary drawing anddescriptions that are not limiting the embodiments of the presentinvention.

FIG. 1 shows a mathematical model of a three-phase induction motor.

FIG. 2 shows stator and rotor magnetic axes of a three-phase inductionmotor.

FIG. 3 shows an equivalent circuit of a pair of stator windings in athree-phase induction motor.

FIG. 4 shows a flow chart of a method to detect faults of a rotarymachine in accordance with the invention.

FIG. 5 shows a block diagram of a preferred embodiment of an apparatusin accordance with the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

In order to explain the invention, a three-phase induction motor hasbeen selected to be the device under test (DUT) shown as 1 in FIG. 5.However, in the contemplated embodiments DUT can be any poly-phase motoror generator with a rotor and at least two stators. FIG. 1 shows amathematical model of the three-phase induction motor, where 101, 102,and 103 are stator windings and 110, 120 and 130 are rotor windings.FIG. 2 shows magnetic axes of the three-phase induction motor, where theangle between stator winding 101, or 102, or 103 and the correspondingrotor winding 110, or 112, or 113 is θ_(r). A three-phase inductionmotor with delta connection can be easily tested by applying an inputsignal to a stator winding and measuring the induced current flowingthrough the stator winding and the voltage across the stator winding. Athree-phase induction motor with star connection typically does not haveneutral connection and can be tested by applying an input signal to astator winding and measuring the induced current from another statorwinding and the voltage across two stator windings, which is shown inFIG. 3 by an equivalent circuit. A three-phase induction motor with starconnection will be further discussed below and the method can be readilyapplied to a three-phase induction motor with delta connection.

During each test, the rotor is stationary and locked at an arbitraryposition.

In the following, the test method and the preferred embodiment of theapparatus will be combined to describe the invention in details.

In step 401 of FIG. 4, an input signal is generated by an arbitrarywaveform generator (AWG) 501 as in FIG. 5. The generated waveform ispreferably a signal covering frequency range from DC to 1 MHz, includinga sinusoidal waveform with sweeping frequency from DC to 1 MHz and otherwideband waveforms. The voltage of the input signal is preferably lowvoltage to medium voltage, for example a peak-to-peak voltage of 3 voltsor 5 volts. The computing and control unit 530 in FIG. 5 controls thewaveform generation. The generated waveform will pass through a lowpassor bandpass filter 502 and a driver 503 in FIG. 5 to improve signalintegrity and drivability.

FIG. 3 shows an equivalent circuit when the stator frame is grounded, aninput signal is applied to stator winding 101, the output current ismeasured from stator winding 102 and the voltage is measured betweenstator winding 101 and 102. However, it is contemplated that there aremany other configurations to test the three-phase induction motor, forexample, one output signal can be the induced voltage on stator winding103. In FIG. 3 R_(s) ¹ is the resistance of stator winding 101 and R_(s)² is the resistance of stator winding 102, L_(s) ¹ is the totalinductance of stator winding 101 and L_(s) ² is the total inductance ofstator winding 102, and C_(s) ¹ is the stator winding-frame capacitanceof stator winding 101 and C_(s) ² is the stator winding-framecapacitance of stator winding 102. In a healthy motor, R_(s) ¹=R_(s)²=R_(s), L_(s) ¹=L_(s) ²=L_(s) and C_(s) ¹=C_(s) ²=C_(s). The current ofstator winding 101 is related to the current of stator winding 102 by I₂¹=−I_(s) ² and the voltage between stator winding 101 and 102 equals toV_(s) ¹−V_(s) ².

The stator winding-frame capacitance is the dominant capacitance amongall stator capacitances. Furthermore, the stator winding-framecapacitance is independent of rotor position. Additionally, the statorwinding-frame capacitance can be measured separately by applying aninput signal between a stator winding and the stator frame, which iswell known from prior art. Thus, the stator winding-frame capacitor canbe treated separately from the total inductance and resistance.

The total inductance of a stator winding includes self-inductance of thestator winding, mutual inductance between the stator winding and otherstator windings, and mutual inductance between the stator winding androtor windings.

In FIG. 5, an input signal is applied to stator windings preferablythrough cable 506 with shield, including coaxial cable and triaxialcable to reduce electromagnetic interference (EMI).

In step 402 of FIG. 4, the output signals will be measured. One outputsignal is preferably the output current from a stator winding, forexample, the output current from stator winding 102 in FIG. 3. Anotheroutput signal is preferably the voltage across stator windings, forexample the voltage across stator winding 101 and 102 in FIG. 3, i.e.V_(s) ¹−V_(s) ²=V_(s) ²=V_(s) ¹², which is essentially proportional tothe input signal voltage. As in FIG. 5, a compensation network 510 isconnected to the stator winding by cable 560, which is preferably acable with shield. For the output current, the compensation network 510converts the output current into an output voltage and enhances theoutput voltage, which comprises two stages. The first stage comprises anarray of resistors and capacitors. The computing and control unit 530dynamically selects the resistors and capacitors to optimize the outputvoltage level and improve signal-to-noise ratio (SNR). One optimizationmethod is to select the resistors and capacitors to match the DUTimpedance which varies with frequency. The second stage comprises avariable-gain amplifier to amplify the output voltage signal to thedesired voltage range so that the measurement accuracy is improved. Thecomputing and control unit 530 dynamically adjust the gain in thevariable-gain amplifier according to the feedback from the measurement.For the voltage across stator windings which is essentially proportionalto the input signal voltage, the compensation network 510 acts as avoltage buffer.

Next the output signals are sampled and converted into digital signalsby ADC 520 in FIG. 5. The ADC preferably has a sampling rate that isequal to or greater than 4 MHz and a resolution that is equal to orbetter than 12 bits. The computing and control unit 530 in FIG. 5controls the ADC 520, receives the digital output signals from ADC 520and calculates the output current and the voltage across the statorwindings.

A frequency response of the system can be defined as the voltage acrossthe tested stator windings divided by the current through the statorwindings, for example H_(s) ¹²=V_(s) ¹²/I_(s) ¹ in FIG. 3. The frequencyresponse is not the impedance of the stator windings only, but acharacteristic quantity of both stator and rotor. The computing andcontrol unit 530 in FIG. 5 performs the frequency response computationby using the measured voltage across stator windings and the measuredoutput current, and separating the stator winding-frame capacitorcontribution. The algorithm used is fast Fourier transform (FFT). Tofulfill the computation, the computing and control unit 530 preferablycomprises a 32-bit central processing unit (CPU), a floating point unit(FPU) and at least 256K SRAM. The computing and control unit 530 can bea microcontroller or a field-programmable gate array (FPGA). To furtherimprove performance, an external memory unit 540 may be added as in FIG.5.

According to the three-phase induction motor model in FIG. 1 and FIG. 2,and Kirchhoff's law,

$V_{s} = {{I_{s}R_{s}} + \frac{d\; \varnothing_{s}}{dt}}$$V_{r} = {{I_{r}R_{r}} + \frac{d\; \varnothing_{r}}{dt}}$$V_{s} = {{\begin{pmatrix}V_{s}^{1} \\V_{s}^{2} \\V_{s}^{3}\end{pmatrix}\mspace{14mu} I_{s}} = {{\begin{pmatrix}I_{s}^{1} \\I_{s}^{2} \\I_{s}^{3}\end{pmatrix}\mspace{14mu} V_{r}} = {{\begin{pmatrix}V_{r}^{1} \\V_{r}^{2} \\V_{r}^{3}\end{pmatrix}\mspace{14mu} I_{r}} = \begin{pmatrix}I_{r}^{1} \\I_{r}^{2} \\I_{r}^{3}\end{pmatrix}}}}$

where V_(s) is the voltage vector of stator windings, I_(s) is thecurrent vector of stator windings, Ø_(s) is the magnetic flux vector ofstator windings, V_(r) is the voltage vector of rotor windings, I_(r) isthe current vector of rotor windings and Ø_(r) is the magnetic fluxvector of rotor windings. The stator winding resistor matrix and therotor winding resistor matrix is

$R_{s} = {{\begin{pmatrix}R_{s} & 0 & 0 \\0 & R_{s} & 0 \\0 & 0 & R_{s}\end{pmatrix}\mspace{14mu} {and}\mspace{14mu} R_{r}} = \begin{pmatrix}R_{r} & 0 & 0 \\0 & R_{r} & 0 \\0 & 0 & R_{r}\end{pmatrix}}$

respectively.

The stator self-inductance matrix, rotor self-inductance matrix andstator-rotor mutual inductance matrix are well-known from prior art.

The stator self-inductance matrix is

$L_{s} = \begin{pmatrix}{L_{ms} + L_{ls}} & {{- \frac{1}{2}}L_{ms}} & {{- \frac{1}{2}}L_{ms}} \\{{- \frac{1}{2}}L_{ms}} & {L_{ms} + L_{ls}} & {{- \frac{1}{2}}L_{ms}} \\{{- \frac{1}{2}}L_{ms}} & {{- \frac{1}{2}}L_{ms}} & {L_{ms} + L_{ls}}\end{pmatrix}$

where L_(ms) is the magnetizing inductance of a stator winding andL_(ls) is the leakage inductance of a stator winding.

With rotor parameters referred to stators, the rotor self-inductancematrix is

$L_{r} = \begin{pmatrix}{L_{ms} + L_{lr}} & {{- \frac{1}{2}}L_{ms}} & {{- \frac{1}{2}}L_{ms}} \\{{- \frac{1}{2}}L_{ms}} & {L_{ms} + L_{lr}} & {{- \frac{1}{2}}L_{ms}} \\{{- \frac{1}{2}}L_{ms}} & {{- \frac{1}{2}}L_{ms}} & {L_{ms} + L_{lr}}\end{pmatrix}$

where L_(lr) is the leakage inductance of a rotor winding.

The mutual inductance between stator and rotor is

$M_{sr} = {L_{ms}\begin{pmatrix}{\cos \mspace{11mu} \theta_{r}} & {\cos\left( {\theta_{r} + {\frac{2}{3}\pi}} \right)} & {\cos\left( {\theta_{r} - {\frac{2}{3}\pi}} \right)} \\{\cos\left( {\theta_{r} - {\frac{2}{3}\pi}} \right)} & {\cos \mspace{11mu} \theta_{r}} & {\cos\left( {\theta_{r} + {\frac{2}{3}\pi}} \right)} \\{\cos\left( {\theta_{r} + {\frac{2}{3}\pi}} \right)} & {\cos\left( {\theta_{r} - {\frac{2}{3}\pi}} \right)} & {\cos \mspace{11mu} \theta_{r}}\end{pmatrix}}$

where θ_(r) is the angle between a stator winding magnetic axis and thecorresponding rotor winding magnetic axis as shown in FIG. 2.

Then we have

Ø_(s) =L _(s) I _(s) +M _(sr) I _(r)

Ø_(r) =L _(r) I _(r) +M _(sr) ^(T) I _(s)

where M_(sr) ^(T) is the transpose of M_(sr).

The rotor winding is shorted so that the voltage across rotor winding iszero. However, there is still current flowing through the rotor due tomutual inductance between stator and rotor. Thus,

V _(r) ¹ =V _(r) ² =V _(r) ³=0

Further, during each test, one stator winding is always open withoutcurrent flowing, for example stator winding 103 in the testconfiguration of FIG. 3. Thus, the Kirchhoff equation on stator winding103 can be removed while stator winding 101 and 102 are being tested.

From the preceding equations, for each test according to the invention,for example the test in FIG. 3, there are five Kirchhoff equations andeight variables V_(s) ¹, V_(s) ², I_(s) ¹, I_(s) ², I_(r) ¹, I_(r) ²,I_(r) ³, θ_(r). The eight variables can be further reduced to sevenvariables V_(s) ¹, V_(s) ¹², I_(s) ¹, I_(r) ¹, I_(r) ², I_(r) ³, θ_(r)using I_(s) ¹=−I_(s) ² and V_(s) ¹−V_(s) ²=V_(s) ¹². Thus, V_(s) ¹² canbe expressed as a function of θ_(r) and I_(s) ¹ via Laplace transform,

$V_{s}^{12} = {{I_{1}^{s}\left( {{2R_{s}} + {3{sL}_{ms}} + {2{sL}_{ls}}} \right)} + {{sI}_{1}^{s}L_{ms}\frac{3\sqrt{3}L_{ms}{\sin \left( {2\theta_{r}} \right)}}{\frac{R_{r}}{S} + {\frac{3}{2}L_{ms}} + L_{lr}}}}$

where s is the complex variable in Laplace transform. The above equationcan be easily transformed into frequency space by s=jω.

Therefore, the frequency response can be calculated,

$H_{s}^{12} = {\frac{V_{s}^{12}}{I_{s}^{1}} = {\left( {{2R_{s}} + {3{sL}_{ms}} + {2{sL}_{ls}}} \right) + {{sL}_{ms}\frac{3\sqrt{3}L_{ms}{\sin \left( {2\theta_{r}} \right)}}{\frac{R_{r}}{S} + {\frac{3}{2}L_{ms}} + L_{lr}}}}}$

Similarly, the frequency responses H_(s) ²³ between stator winding 102and 103 and H_(s) ³¹ between stator winding 103 and 101 can be obtained.

It is apparent that the frequency response depends on rotor positionangle θ_(r).

In Step 403 of FIG. 4, a derived quantity is calculated from thefrequency responses so that the derived quantity is independent of rotorangle θ_(r). There are two derived quantities

${DQ}_{1} = {\frac{H_{s}^{12} + H_{s}^{23} + H_{s}^{31}}{3} = {{2R_{s}} + {3{sL}_{ms}} + {2{sL}_{ls}\mspace{14mu} {and}}}}$${DQ}_{2} = {\sqrt{\left( {H_{s}^{12} - {DQ}_{1}} \right)^{2} + \frac{\left( {H_{s}^{23} - H_{s}^{31}} \right)^{2}}{3}} = {{sL}_{ms}\frac{3\sqrt{3}L_{ms}}{\frac{R_{r}}{s} + {\frac{3}{2}L_{ms}} + L_{lr}}}}$

The computing and control unit 530 calculates H_(s) ¹², H_(s) ²³ andH_(s) ³¹ from the measurements of V_(s) ¹² and I_(s) ¹. The computingand control unit 530 further calculates DQ₁ and DQ₂ by aforementionedequations. DQ₁ and DQ₂ are independent of rotor position and arecharacteristics of the three-phase induction motor.

In addition, the rotor winding position angle relative to stator windingcan be obtained by

${\tan \left( {2\theta_{r}} \right)} = \frac{\sqrt{3}\left( {H_{s}^{12} - {DQ}_{1}} \right)}{H_{s}^{23} - H_{s}^{31}}$

In general, for a stator with N windings, the number of derivedquantities is N−1 and the rotor position angle can be obtainedsimultaneously.

It is also contemplated that the inductance and resistance in DQ₁ andDQ₂ are frequency dependent, due to eddy-currents in the core, and skinand proximity effect in the windings.

An advantage of the above-mentioned method and apparatus is that arotary machine can be tested at any rotor position, which significantlysimplifies the test and apparatus design. Furthermore, DQ₁ and DQ₂ arethe unique identities of the three-phase induction motor and areindependent of rotor position.

In step 404 of FIG. 4, DQ₁ and DQ₂ are compared with correspondingreference quantities.

The reference quantities can be derived using the same method andapparatus while the test is done with the rotor at a different position,or the test is done in a different time period, for example right afterthe motor is purchased and calibrated, or the test is done on areference motor of the same type. Therefore, there are multiple ways tocompare a derived quantity with the corresponding reference quantity.

In case that there is any fault in the motor, the space symmetry of thestator or rotor is broken, which causes DQ₁ and DQ₂ to becomerotor-position dependent and deviate from the reference quantities.Thus, a fault can be detected by comparing DQ₁ and DQ₂ withcorresponding reference quantities. The reference quantities can bestored in an external storage 504, which is connected to the computingand control unit 530 as in FIG. 5.

The comparison comprises a statistical method including statisticalhypothesis tests, mean comparison, standard deviation comparison, andother statistical comparison methods. The statistical method preferablycomprises a statistical hypothesis test including Student's t-test,F-test, and analysis of variance (ANOVA). It is preferred that each testis performed more than three times by repeating step 401-403. Similarlyeach reference quantity is preferred to have more than three datapoints. Thus, the statistical test is more reliable when comparing thetwo populations.

Furthermore, DQ₁ and DQ₂ comprise magnitude and phase. Both of magnitudeand phase are compared. In addition, the comparison covers a wide rangeof frequency for each derived quantity. Depending on the failure mode,the derived quantity can be more sensitive at a certain frequency, whichincreases the sensitivity of the detection. Thus, with multiplecomparisons done on different derived quantities and across differentfrequencies, the fault detection is significantly more robust.

In step 405 of FIG. 4, a decision is made that there is a fault in themotor at a certain confidence level if the statistical hypothesis testshows significant difference between DQ₁ or DQ₂ and the correspondingreference quantity. A significant level of 0.05 is typically used andthe corresponding confidence level is 95%. Thus, we are 95% confidentthat the motor has a fault if the statistical hypotheses test shows asignificant difference at the significant level of 0.05.

By using the statistical hypotheses test, the interpretation of the testdata is more reliable, and the subjective judgment and errors areeliminated in evaluating motor state. With confidence level clearlyprovided, the user has more confidence in evaluating the rotary machinestate.

At the end of the test, all the raw data and calculated quantities canbe formatted and conveniently stored in an external storage 504 of FIG.5, for example a USB flash drive.

A display 505 of FIG. 5 is further used to display results and exchangeinformation with the user. The display 505 is connected and controlledby the computing and control unit 530 as in FIG. 5.

A significant change in temperature can shift the test results. In FIG.5 a temperature sensor 550 is connected to the computing and controlunit 530, which records the temperature and saves it together with othertest data.

The detailed description of the disclosure is to enable any personskilled in the art to make or use the disclosure. It is contemplatedthat there are various modifications of the preferred embodimentdescribed herein, which are still within the scope of the claims of theinvention. Thus, the disclosure is not limited to the preferredembodiment described herein.

OTHER PUBLICATIONS

-   L. Lamarre and P. Picher. “Impedance characterization of hydro    generator stator windings and preliminary results of FRA analysis.”    in Proc. Conf. Record 2008. IEEE Int. Symp. Electr. Insul., pp.    227-230.-   Martin Brandt. Slavomír Kascak, “Failure Identification of Induction    Motor using SFRA Method”, in ELEKTRO 2016, pp 269-272

What is claimed is:
 1. An off-line method for detecting faults in arotary machine having a rotor and at least two stator windings, themethod comprising the steps of: (a) generating, with a signal generator,an input signal and applying said input signal to a stator winding or aset of stator windings of said rotary machine while said rotor is lockedat a rotor position; (b) measuring a current and a voltage, with an ADCand a computing and control unit, from said stator winding or said setof stator windings while said rotor is locked at said rotor position;(c) applying Fourier transform, with said computing and control unit, tosaid current and said voltage to obtain a frequency response of saidstator winding or said set of stator windings at said rotor position;(d) repeating the method from step (a)-(c) to obtain frequency responsesof all stator windings or all sets of stator windings; (e) formingderived quantities, with said computing and control unit, from all saidfrequency responses so that said derived quantities are independent ofsaid rotor position; (f) comparing, with said computing and controlunit, a magnitude or a phase difference between said derived quantitiesand corresponding reference quantities; (g) determining, with saidcomputing and control unit, that there is a fault in said rotary machineif said magnitude or said phase difference exceeds a threshold number.2. The method of claim 1, wherein said input signal comprises anarbitrary waveform including a sweeping frequency waveform, an impulsewaveform, a maximum length binary sequence (MLBS) waveform and otherwideband waveforms.
 3. (canceled)
 4. (canceled)
 5. (canceled)
 6. Themethod of claim 1, wherein said corresponding reference quantities arederived on said rotary machine by following step (a)-(e) while saidrotor is locked at another rotor position, or said correspondingreference quantities are derived on said rotary machine in a differenttime period by following step (a)-(e), or said corresponding referencequantities are derived on a reference rotary machine of the same type byfollowing step (a)-(e).
 7. (canceled)
 8. (canceled)
 9. (canceled)
 10. Anapparatus for off-line fault detection in a rotary machine having arotor and at least two stator windings, the apparatus comprising atleast a signal generator, an ADC, and a computing and control unit toperform the functions of: (a) generating an input signal and applyingsaid input signal to a stator winding or a set of stator windings ofsaid rotary machine while said rotor is locked at a rotor position; (b)measuring a current and a voltage from said stator winding or said setof stator windings while said rotor is locked at said rotor position;(c) applying Fourier transform to said current and said voltage toobtain a frequency response of said stator winding or said set of statorwindings at said rotor position; (d) repeating step (a)-(c) to obtainfrequency responses of all stator windings or all sets of statorwindings; (e) forming derived quantities from all said frequencyresponses so that said derived quantities are independent of said rotorposition; comparing a magnitude or a phase difference between saidderived quantities and corresponding reference quantities; (g)determining that there is a fault in said rotary machine if saidmagnitude or said phase difference exceeds a threshold number.
 11. Theapparatus of claim 10, wherein said input signal comprises an arbitrarywaveform including a sweeping frequency waveform, an impulse waveform, amaximum length binary sequence (MLBS) waveform and other widebandwaveforms.
 12. (canceled)
 13. (canceled)
 14. (canceled)
 15. Theapparatus of claim 10, wherein said corresponding reference quantitiesare calculated on said rotary machine by following step (a)-(e) whilesaid rotor is locked at another rotor position, or said correspondingreference quantities are calculated on said rotary machine in adifferent time period by following step (a)-(e), or said correspondingreference quantities are calculated on a reference rotary machine of thesame type by following step (a)-(e).
 16. (canceled)
 17. (canceled) 18.(canceled)